The Brachistochrone problem was posed by Johann Bernoulli as a challenge in 1697. It is still an appropriate problem as an example for application in many branches of mathematics. The problem was first solved by Newton in 1697 itself. Later this problem was solved by using Euler-Lagrange equation with the Calculus of Variations. Now this same problem is solved, in the recent years, by using the Fractional Calculus of Variations.